All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
[This ruling is based on the woman being a Muslim]
First of all, it should be noted that in principle a Muslim is innocent [until he/she is proven guilty], so it is not permissible to accuse him/her of Zina (fornication or adultery) directly or indirectly. Allaah says (what means): {Verily, those who accuse chaste women, who never even think of anything touching their chastity and are good believers, are cursed in this life and in the Hereafter, and for them will be a great torment.} [Quran 24: 23]. Allaah further says (what means): {O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin.} [Quran 49:12].
Therefore, it is not permissible for this man to ask this woman to prove her virginity. This is a disgraceful behaviour that a noble man would not ask for as it is an indirect accusation for her having committed Zina. The Hanafi jurists are of the view that indirectly accusing a woman of Zina is an open accusation of same, but they do not consider that the corporal punishment determined by the Islamic Law should be applied on the accuser because of doubt [that one is accusing her of Zina]. However, the Maaliki jurists are of the view that indirectly accusing a woman of Zina, if it is understood that it is an open accusation because of the existence of some circumstances like a dispute, or the like, then this is considered as an open accusation and they are of the view that the corporal punishment determined by the Islamic Law should be applied on the accuser.
Finally, it should be noted that it is not permissible for this woman to consult a male or female doctor for this purpose as it requires looking at her 'Awrah (parts of the body that must be covered in Islam) [and in this case looking into her vagina] and it is not permissible to look at the 'Awrah [of another person] except for a necessity or a dire need. In this case, there is no necessity or a dire need. This woman is in principle innocent.
Furthermore, it should be noted that a woman could lose her virginity because of other reasons than Zina. She could lose her virginity by the strong flow of the blood of her menses or by a sudden jump and the like.
Allaah Knows best.